# Direct Bias-Correction Term Estimation for Average Treatment Effect Estimation

arXiv: https://arxiv.org/abs/2509.22122 · HTML: https://mlsanity.com/paper/2509.22122/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 56 references that are in the map.
- First posted on arXiv 26 Sep 2025.

## Builds on (most cited first, 8 of 8)

- [Adapting Neural Networks for the Estimation of Treatment Effects](https://mlsanity.com/paper/1906.02120/) (2019)
- [Telescoping Density-Ratio Estimation](https://mlsanity.com/paper/2006.12204/) (2020)
- [Approximate Residual Balancing: De-Biased Inference of Average Treatment Effects in High Dimensions](https://mlsanity.com/paper/1604.07125/) (2016)
- [Non-Negative Bregman Divergence Minimization for Deep Direct Density Ratio Estimation](https://mlsanity.com/paper/2006.06979/) (2020)
- [RieszNet and ForestRiesz: Automatic Debiased Machine Learning with Neural Nets and Random Forests](https://mlsanity.com/paper/2110.03031/) (2021)
- [Covariate Balancing Propensity Score by Tailored Loss Functions](https://mlsanity.com/paper/1601.05890/) (2016)
- [Augmented balancing weights as linear regression](https://mlsanity.com/paper/2304.14545/) (2023)
- [Automatic Debiased Machine Learning for Covariate Shifts](https://mlsanity.com/paper/2307.04527/) (2023)

## Built on by (most cited first, 9 of 9)

- [Nearest Neighbor Matching as Least Squares Density Ratio Estimation and Riesz Regression](https://mlsanity.com/paper/2510.24433/) (2025)
- [Direct Debiased Machine Learning via Bregman Divergence Minimization](https://mlsanity.com/paper/2510.23534/) (2025)
- [Riesz Regression As Direct Density Ratio Estimation](https://mlsanity.com/paper/2511.04568/) (2025)
- [A Unified Theory for Causal Inference: Direct Debiased Machine Learning via Bregman-Riesz Regression](https://mlsanity.com/paper/2510.26783/) (2025)
- [Semi-Supervised Treatment Effect Estimation with Unlabeled Covariates for Prediction-Powered Causal Inference](https://mlsanity.com/paper/2511.08303/) (2025)
- [Bridging the Gap between Empirical Welfare Maximization and Conditional Average Treatment Effect Estimation in Policy Learning](https://mlsanity.com/paper/2510.26723/) (2025)
- [genriesz: A Python Package for Automatic Debiased Machine Learning with Generalized Riesz Regression](https://mlsanity.com/paper/2602.17543/) (2026)
- [Covariate Balancing and Riesz Regression Should Be Guided by the Neyman Orthogonal Score in Debiased Machine Learning](https://mlsanity.com/paper/2605.06386/) (2026)
- [Prediction-Powered Causal Inference by Automatic Debiased Machine Learning and Semi-Supervised Riesz Regression](https://mlsanity.com/paper/2606.12892/) (2026)

## Abstract (arXiv)

This study considers the estimation of the direct bias-correction term for estimating the average treatment effect (ATE). Let (Xi, Di, Yi)i=1n be the observations, where Xi denotes K-dimensional covariates, Di ∈ 0, 1 denotes a binary treatment assignment indicator, and Yi denotes an outcome. In ATE estimation, h0(Di, Xi) = frac1[Di = 1]e0(Xi) - frac1[Di = 0]1 - e0(Xi) is called the bias-correction term, where e0(Xi) is the propensity score. The bias-correction term is also referred to as the Riesz representer or clever covariates, depending on the literature, and plays an important role in construction of efficient ATE estimators. In this study, we propose estimating h0 by directly minimizing the Bregman divergence between its model and h0, which includes squared error and Kullback--Leibler divergence as special cases. Our proposed method is inspired by direct density ratio estimation methods and generalizes existing bias-correction term estimation methods, such as covariate balancing weights, Riesz regression, and nearest neighbor matching. Importantly, under specific choices of bias-correction term models and Bregman divergence, we can automatically ensure the covariate balancing property. Thus, our study provides a practical modeling and estimation approach through a generalization of existing methods.